Question

Two sides of a triangle are 16.2 cm and 29.6 cm, with the included angle 106◦. What is angle opposite the side 16.2 cm?

Answer 1

The angle `A ~~ 24.6^@`

Explanation:

Let side `a = 16.2" cm"`
Let side `b = 29.6" cm"`
Let side `c =` the unknown side.

Let `angle A =` the unknown angle opposite side a.
Let `angle B =` the unknown angle opposite side b.
Let `angle C = 106^@`

Use the Law of Cosines to find the length of side c:

`c = sqrt(a^2 + b^2 - 2(a)(c)cos(C))`

`c = sqrt((16.2" cm")^2 + (29.6" cm")^2 - 2(16.2" cm")(29.6" cm")cos(106^@))`

`c ~~ 37.46" cm"`

Use the Law of Sines to find `angle A`

`sin(A)/a = sin(C)/c`

`sin(A) = sin(C)a/c`

`A = sin^-1(sin(C)a/c)`

`A = sin^-1(sin(106^@)(16.2" cm")/(37.46" cm"))`

`A ~~ 24.6^@`